What exactly does Darwin's theory state and how it is different from Punctuated Equilibrium?If Darwin's theory states that evolution occurs in a...

Darwin believed that evolution was a slow, gradual
continuous process of change.  This could mean that evolutionary changes could occur
over thousands or hundreds of thousands of years.  It is so gradual that one cannot
detect these changes in a lifetime, or even over several generations.  Punctuated
Equilibrium is not the opposite of Darwin’s Theory of Evolution.  It is really more of a
variation of the Theory of Evolution.  The big difference is the time it takes for
evolutionary changes to occur.  Darwin thought that evolution was slow and gradual.  If
so, then these gradual changes should show up in the fossil record.  They do not, and
this did bother Darwin.  He simply thought that the fossil record was incomplete.
Punctuated Equilibrium was an idea that was proposed by Stephen Jay Gould and Niles
Eldredge in 1972.  It was a critique of Darwin’s Theory of Evolution.  Whereas Darwin
believed that evolution was a slow process that continued on without any sudden changes,
Eldredge and Gould believed that evolution happened in “fits and starts”—that is, that
evolutionary changes sometimes moved quickly, and at other times it didn’t move at all
or moved extremely slowly.  When evolutionary changes came slowly or not at all, there
was “equilibrium”.  These periods of “equilibrium” were “punctuated” with times of very
fast changes or developments; therefore, evolution was not a slow, continuous
process.